I.C. Goumans s1703609
Prof. Dr. F. Picchioni Prof. A.D. Gotsis
University of Groningen Department of Chemical Engineering
This thesis describes the research that is performed towards the free radical melt modification of long chain branched (LCB) isotactic-Polypropylene (iPP). The synthesis and characterization of LCB-iPP was performed. For reference, chapter 2 captures an overview of the available and useful literature regarding the branching process and the science of rheology.
The synthesis and characterization of LCB-iPP is described in chapter 3. The synthesis was carried out with dicumyl peroxide as free radical initiator and five selected co-agents. The characterization was performed by differential scanning calorimetry (DSC), gel permeation chromatography (GPC) and rheological measurements.
An attempt was made to quantitatively correlate the co-agent properties with the zero shear viscosity, but it was not possible to fit the data in statistically significant way. Nevertheless, at a more qualitative level, few important co-agent properties were defined and a ranking of the use co-agents regarding their ability in inducing long chain branches is presented. It was found that hydroquinone (HQ) resulted in modified iPP with the highest degree of branching while allyl-2-furoate (A2F) was not capable of inducing a branched structure.
Regarding the choice of co-agent, a wide range of different molecules can be used. Many different co-agents which are capable of inducing a branched structure can be found in literature. Various strategies have been proposed to restrain the degradation of iPP and suppress crosslinking during the melt modification. However, to our knowledge, a systematic study towards the choice of co-agent has not been performed yet. This gives rise to the question; what are key features for inducing a branched structure? In this work a systematic study towards the choice of co-agent was performed and few important co-agent properties were defined which can be used for selecting a co-agent.
This report is the result of my graduation project for the completion of my education Chemical Engineering at the University of Groningen. Although the progress of the project didn’t go as planned, it was a very useful experience and I enjoyed the time working on it.
There are a few people I would like to thank personally, starting with professor Francesco Picchioni, for his continuously support. His enthusiasm provided me with a lot of energy and motivation. In every discussion, he challenged me to look further and beyond the obvious. I really enjoyed working with him.
I would also like to thank professor Alexandros Gotsis, for all his help and support during my time in Chania, Crete. He put a lot of time and effort in making rheology understandable.
Furthermore, I would like to thank Martijn Beljaars for his support and for ordering all my chemicals.
My sincere thanks also go to Gert Alberda, who provided help with the DSC measurements and Andries Jekel for the GPC measurements. And, last but not least, I would like to thank my fellow students for the great atmosphere and the discussions.
Table of Contents
Summary ... 1
Acknowledgements ... 2
1 Introduction ... 5
1.1 Long chain branched iPP ... 5
1.2 Aim and scope ... 7
1.3 Relevance ... 7
2 Long chain branched i-polypropylene ... 8
2.1 Introduction ... 8
2.2 Melt modification ... 8
2.2.1 Factors influencing the process... 10
2.3 Characterization of the resulting structure ... 12
2.3.1 Gel permeation chromatography (GPC) ... 12
2.3.2 Shear rheology ... 13
2.3.3 Extensional rheology ... 17
3 Synthesis and characterization of long chain branched i-polypropylene ... 20
3.1 Abstract ... 20
3.2 Introduction ... 20
3.3 Experimental ... 22
3.3.1 Materials ... 22
3.3.2 Preparation of the samples ... 22
3.3.3 Thermal behavior, molecular weight and gel content determination ... 23
3.3.4 Dynamic shear measurements ... 23
3.3.5 Extension viscosity measurements ... 24
3.4 Results and discussion ... 24
3.5 Conclusions ... 42
4 Final remarks ... 43
Bibliography ... 44
Appendix A ... 49
Appendix B ... 51
Appendix C ... 52
1.1 Long chain branched iPP
Isotactic polypropylene (iPP) is one of the most widely used thermoplastics in the world. This is due to the desirable and beneficial physical properties, such as low density, good heat and chemical resistance, high melting temperature, stiffness and the reusability. Commercial iPP is produced by using metallocene or classical Ziegler-Natta catalytic systems, which results in highly linear chains with a relatively narrow molecular weight distribution. As a consequence, commercial iPP shows low melt strength and weak strain hardening behavior. Many process techniques, like foaming, blow molding, thermoforming, injection molding and spinning, require strain hardening behavior. This can be obtained by introducing long chain branches or broadening the molecular weight distribution. Although the effects of broadening the molecular weight distribution (polydispersity) and long chain branching are pointing in the same direction, the latter is much stronger and more efficient to enhance the melt strength of polymers .
So far there are four ways to produce LCB-iPP, through direct synthesis  , through solid state modification , by electron beam irradiation  and through melt modification      
        .
The direct synthesis of LCB-iPP is carried out using metallocene catalysis directly  or via the addition of pre-made iPP macro-monomers . In situ polymerization provides control of the stereochemistry and molecular weight of the LCB-iPP. However, disadvantages of catalytic systems are high costs and reactor fouling.
Another method is the modification by peroxide reactions in the solid state in the presence or absence of a co-agent . The main advantages of this method are restrained β-scission and more control over the process. A disadvantage, however, is the long reaction time which results in low productivity when implemented in industry.
Electron beam irradiation is a popular method because it can be easily used in industry .
However, electron beam irradiation produces LCB-iPP with broadened molecular weight distribution and complex branch structures .
In this research the modification is carried out in the melt by radical reaction. The major advantages of melt modification are low costs, simple operation and high productivity when implied in industry .
However, the melt modification also faces a lot of difficulties due to the many side reactions which make it difficult to control the process. A general scheme of the radical reactions taking place in the modification can be seen in figure 1.
Figure 1: General scheme of the radical reactions (based on )
A detailed discussion of this general mechanism will be presented in the following chapters.
1.2 Aim and scope
In this thesis isotactic polypropylene (iPP) is modified with long chain branches in the melt through radical reaction. The long chain branches are linked to the iPP backbone with the help of a bi-functional co-agent which acts as a chemical bridge.
A lot of effort in producing branched iPP is performed in the polymer industry and several commercial grades of high melt strength iPP are available . A lot of different co-agents were used for inducing a branched structure to obtain strain hardening behavior. However, to our knowledge, no systematic study towards the choice of co-agent has been performed.
Therefore, the main aim of this thesis is to examine which co-agent is most effective in inducing long chain branches when used in the melt modification and which properties of the co-agent are key features to obtain the desired branched structure. A more accurate understanding of the chemical mechanism involved in the process (co-agent reactions) is required and the factors that have significant influence on the process need to be defined.
The synthesis of the long chain branched (LCB) iPP is carried out through radical melt reaction. The synthesis method is based on existing literature. An overview of the literature is presented in chapter 2.
The characterization of the product is performed by differential scanning calorimetry (DSC), gel permeation chromatography (GPC), gel content determination and rheology measurements. DSC, GPC and gel content determination give an indication of the existence of LCB, but rheology measurements are used to verify that long chain branches really exist on the backbone of the chain.
The relevance of this research project is provided in the remainder of this chapter. An overview of the literature on the synthesis and rheology is given in chapter 2. The remainder of this thesis presents the obtained research results.
In the last decades, the polymer industry has put a lot of effort in producing branched iPP. The desirable properties of iPP render it one of the most widely used polymers in the world. However, conventional linear iPP has poor melt strength and cannot easily be used in processes where elongational flow is dominant. Unfortunately, there are a lot of industrial situations where there is a large element of extensional flow, such as foaming, blow moulding and spinning. It is therefore expected that the improvement of the elongational flow behavior will substantially contribute to the growth of this polymer in the plastics market . The major advantages of the melt modification are low costs, simple operation and high productivity. It is therefore desirable for the polymer industry to gain more insight and control over the melt process.
2 Long chain branched i-polypropylene
This chapter gives an overview of available literature on the synthesis and rheology relevant for the remainder of this thesis.
Branching and/or crosslinking of polyolefins is usually carried out by the formation of a non-terminal macro-radical, which can recombine with another macro-radical to form the desired structure. The macro-radicals can be produced by hydrogen atom extraction by a radical initiator (peroxide) or through direct scission of the chemical bonds present in the chain structure (ϒ-rays, electron beam) .
However, when iPP is treated with a radical initiator it degrades through β-scission. To restrain β- scission, a bi-functional co-agent can be added to the system which reacts with the macro-radical to form a more stable adduct.
The introduction of branches has dramatic effects on the rheological properties of the material in the molten state. More entanglement points are present in LCB-iPP, making the material more elastic.
This is mainly measured by a frequency sweep experiment. The branches also give rise to strain hardening behavior which is measured with a controlled strain rate rheometer.
2.2 Melt modification
Melt processing of iPP is an attractive synthetic approach to create LCB-iPP. Peroxide initiated chain scission and co-agent assisted linking transforms the architecture of linear iPP into LCB-iPP. The advantages of melt modification lie in the low costs, simple operation and high productivity when implemented in industry. However, melt modification also has his disadvantages; the many side reactions make it difficult to control the process. A general accepted reaction mechanism (with divinylbenzene as co-agent) can be found in figure 2 .
Figure 2: General accepted reaction mechanism with divinylbenzene as co-agent
Through decomposition of the peroxide, primary radicals are formed which react with iPP to form macro-radicals. The macro-radicals are not stable and can in principle undergo two main reactions, degradation (β-scission) or stabilization with a co-agent to form the more stable adduct (7). The higher stability of the adduct (7) is provided through the existence of resonance structures. The free radical will abstract a hydrogen from a polypropylene chain forming the grafted adduct (8) which can further react to form the desired long chain branches. At the same time a lot of side reactions are taking place, with crosslinking being the most undesired. The following side reactions can take place :
- Hydrogen abstraction with the initiator instead of the iPP chain - Direct coupling of two tertiary macro-radicals
- Coupling of the grafted adduct (8) with a tertiary macro-radical
10 - Homo- and graft- polymerization of the co-agent (initiation by primary radical and macro-
- Transfer of radical species to the initiator or co-agent
The direct or indirect coupling of tertiary macro-radicals and the direct coupling between two non- terminal macro-radicals leads to the formation of cross-linked polypropylene. To avoid the formation of cross-linked material, β-scission is necessary to ensure that there are enough shorter iPP chains to react with the grafted adduct. This is also demonstrated by blank experiments .
Through the years a lot of effort is carried out to control the branching reaction. Various processes are proposed to restrict degradation and prevent crosslinking, like prolonging the lifetime of macro- radicals by reacting with dithiocarbamate radicals reversibly    and stabilizing macro-radicals by changing radical intermediate states using styrene  or furan derivatives . Unfortunately these methods are not able to fully prevent crosslinking and have little effect on the branching degree.
Another drawback, of the above mentioned processes, is that besides a co-agent and peroxide the addition of one more “assisting” agent is necessary to produce the LCB-iPP.
Gotsis and Zeevenhoven  used special peroxydicarbonates to synthesize long chain branches on the polypropylene backbone. The peroxydicarbonates used in this research not only provided the radicals in the mixture but also functioned as the chemical bridge (co-agent) between the polypropylene chains. Many more processes have been proposed to produce LCB-iPP. An overview of these processes providing used peroxides and co-agents is given in Appendix A.
Crosslinking and branching are competing reactions. Over the years, a lot of research is performed towards the crosslinking of iPP in the melt through radical reactions (with or without the use of a co- agent). Relevant information about the mechanism, use of co-agent and amount of peroxide used can therefore be found in literature about crosslinking of iPP as well.
2.2.1 Factors influencing the process
The control of the final structure is of relevant importance in the synthesis of LCB-iPP. The best process conditions are required to get the desired final structure, limit β-scission and avoid crosslinking.
The final structure is determined by reaction parameters such as temperature, co-agent structure, feed composition and duration. A full understanding of the significant influence of these parameters has not been reached yet, but many aspects are under reasonable control and are discussed here.
Thermal degradation of the polypropylene chain proceeds by oxidative processes or simply by the action of heat . A higher temperature results in more degraded material and therefore a lower molecular weight. The effect of oxygen (air) on the thermal degradation depends on the mechanisms of polymerization. Beyler and Hirschler  state that free radical polymerization leads to neutralization of the effect of oxygen. As a result, less degradation takes place when radicals are presented in the system.
Chodák and Zimányová  investigated the effect of temperature on peroxide initiated crosslinking of polypropylene. They observed a decrease of crosslinking efficiency with increasing temperature.
These findings support the view that higher temperature increases the rate of fragmentation, due to the higher activation energy of that process, compared with that for macro-radical recombination .
11 Amount of co-agent and peroxide
Fragmentation (β-scission) is in principle a first order reaction while recombination (crosslinking) of the macro-radicals is of the second order of magnitude. Therefore a higher amount of macro-radicals in the mixture favors the crosslinking reaction   .
It is known that radical activity is more intense amongst the largest chains . Therefore the co- agent is preferentially grafted to high molecular weight chains. Furthermore, the grafting of a co-agent onto the polypropylene chain makes the chain more reactive with respect to molecular weight growth  and therefore has a more prominent tendency towards crosslinking. Based on these arguments, it can be stated that a cross-linked structure is more likely to occur when a higher amount of co-agent is used.
Last but not least, the reactivity of the co-agent needs to be considered when determining the amount of co-agent and peroxide. A high reactive co-agent requires a lower amount of peroxide for branching to occur while a less reactive co-agent requires a higher amount of peroxide .
Coupling of the co-agent and β-scission is required to obtain the desired branched structure.
Therefore, the best results are most likely found with a low amount of high reactive co-agent and a low amount of peroxide. These theoretical considerations are in agreement with the results obtained by Wang et al. .
Co-agent structure and reactivity
Regarding the choice of co-agent, a wide range of different molecules can be used. The selected co- agent needs two double bonds able to react with the formed macro-radicals and at least be bi- functional. Other important properties towards the branching process are solubility in the melt, reactivity of the co-agent, stability of the formed radical and susceptibility towards homo- polymerization.
When the co-agent is not fully soluble in the polypropylene melt, the reaction mainly occurs at the interface and is therefore affected by mixing efficiency and screw design of the extruder . To ensure good solubility of the co-agent in the polypropylene melt, the solubility parameters need to be in the same range.
A co-agent with a high reactivity (towards iPP) grafts relatively fast on the polypropylene chain in comparison with a low reactive co-agent. High reactivity therefore stabilizes the macro-radicals and limits degradation. But according to Parent et al.  the grafting increases the capacity for crosslinking, meaning that a high reactivity leads to a cross-linked structure. In order to suppress crosslinking and promote branching, a co-agent with two different reactive double bonds can be used. Zhang et al. 
demonstrated that the higher reactive double bond preferentially reacts with macro-radicals to stabilize the macro-radicals quickly, while the lower reactive double bond will later react with the secondary radical, formed through β-scission, to avoid the formation of hyper-branched or even cross-linked structure. This method promotes the formation of LCB structure and shows a more uniform distribution of branching and molecular weight.
Furthermore, Chodák et al.  stated that the more stable co-agent radical, after recombination with the macro-radicals, leads to a rise of the polymer molecular weight, while a co-agent that is highly reactive towards itself will result in inefficient consumption of the co-agent.
2.3 Characterization of the resulting structure
Long chain branches are modified onto the iPP backbone to improve the melt behavior during processing. Characterization of the resulting structure is performed to verify the existence of LCB-iPP.
The molecular parameters that are important for the processing properties include the average number of branches per molecule (Bn), their topology (the distribution along the chain and their comb- or Cayley tree type structure) and their lengths . There are three main methods to detect the long chain branches, namely nuclear magnetic resonance (NMR), triple sensor gel permeation chromatography (GPC) and rheology measurements, the latter being the most reliable. The first method can detect branches through the resonance peak of the methine carbon. Detection of this methine resonance peak corresponds to branches longer than four carbons . Unfortunately, ordinary NMR isn’t capable of detecting the small amount of LCB that is needed for enhancement of the melt strength. Therefore this method is not used in this research. Triple sensor GPC and rheology are discussed below in more detail.
2.3.1 Gel permeation chromatography (GPC)
Gel permeation chromatography (GPC) is a type of size-exclusion chromatography that separates the sample on the basis of size. The separation is based on the hydrodynamic volume of the sample, from which one can calculate the molecular mass and its distribution. Branched chains are denser in solution than linear chains of the same molecular weight. Therefore having a lower radius of gyration ( ) and intrinsic viscosity . An estimate of the amount of LCB can be determined from the means square radius of gyration and intrinsic viscosity. The fundament of this method is established by Zimm and Stockmeyer . They expressed the following branching factors:
Here the captions br and lin represent branched and linear chains. The relationship of g and g’ can be expressed by:
(2.3) Here takes values between 0.5 and 1.5 . For random branching, a value of 0.75 is often used and from this the average number of branches per polymer, Bn, can be calculated, by solving the following equation :
13 2.3.2 Shear rheology
Polymers show viscoelastic behavior. Typical viscoelastic behavior can be described best with the Burgers model (figure 3). When a force is applied the initial response will be the immediate elastic response (G1). Then there is a delayed elastic response, which can be described as a spring and dashpot in series (G2 and Ƞ2). The deformation rate here becomes slower and slower until a steady state is reached. This steady state is the viscous response of the model and described by the last dashpot (Ƞ1).
This model shows that the elastic modulus, G, can be described by an immediate elastic response and a delayed elastic response. The immediate solid like response is called the storage modulus, G’, the delayed liquid like response is called the loss modulus G’’.
Figure 3: Simple mechanical models describing viscoelastic behavior 
Viscoelastic behavior can be analyzed with shear rheology. During an oscillatory test a sine-wave- shaped input of strain, , results in a sinusoidal strain output which can be described as:
Where is the strain amplitude and ω is the angular frequency. The stress can be described in the same way. However, in a viscoelastic material the stress, , is partly damped by the viscous response of the material which results in a shift by a phase angle δ.
Where is the yield stress. During the shear measurements, the viscoelastic material undergoes an in phase solid like response and a corresponding liquid like response which is π/2 out of phase with the
14 input . Equation 2.6 can be rewritten by using trigonometry, which results in the following equation :
The storage modulus G’ and the loss modulus G’’ can now be defined as:
With the loss tangent:
The G’ and G’’ produced during the measurements are sometimes reported in different ways, for instance :
From the dynamic viscosity the zero-shear rate viscosity can be estimated by :
(2.14) The rheology of polymer melts is controlled by molecular weight distribution, degree of branching, temperature and pressure . When additives, such as plasticizers, are used, the concentration is also a factor that controls the rheology. Polymer melts are elastic because tension in the chains between entanglements persists while the entangled chains slide over each other . The onset of entanglements is called the critical molecular weight of the polymer, , and this point depends on the chain configuration.
The existence of entanglements makes flow more difficult and therefore the viscosity dramatically increases from the onset of entanglements. This increase in viscosity can be described according to the following equation:
The factors that control the rheology of a polymer melt can often be incorporated into a single master curve by plotting the non-dimensional quantity against , where α is a constant near
15 unity, ρ is the polymer density at T, the temperature in Kelvin . According to this relation, the broadening of the molecular weight results in a polymer melt behaving non-Newtonian at lower values of shear rate. A similar effect can be seen for the addition of branches onto a polymer backbone. The addition of branches onto a polymer backbone results in a more compact chain (figure 4), this generally results in a lower viscosity in the melt at high shear rates.
Figure 4: Isolated polymer coils 
The addition of long chain branches or broadening the molecular weight increases the possibility for entanglements and thus increases the elasticity. Long chain branches make it difficult for the chains to move at low shear rates and therefore the zero shear viscosity increases, something that is not true for broadening the molecular weight distribution.
According to Tsenoglou and Gotsis  this increase in zero shear viscosity, Ƞ0, can be related to the average number of branches per molecule, Bn, with the following equation:
Where is the molecular weight of the linear component, = 13640 g/mole for polypropylene  and α is a constant independent of the branching point functionality and equal to 15/8  . The molecular weight dependence of the viscosity of the linear component can be described according to the following equation:
(2.17) Where , with being the molecular weight between two successive entanglements. For PP, is roughly equal to 5600 and is the melt viscosity at the entanglement crossover, where
. Now equation 2.16 can be restated as follows:
In order to use this method for determining the long chain branches, the zero shear viscosity, , needs to be determined. The is calculated from the Cross three-parameter fitting equation :
16 (2.19) Where ʎ is a material constant with units of time and is related to the power law index. But this method is not so straightforward, because the zero shear viscosity depends on the molar mass as well. It is expected, as discussed earlier, that the viscosity of a linear polymer should follow a 3.4 power-law dependence on molar mass. As a consequence of this, linear polymers with the same value would have about the same viscosity if they had the same . Since the generation of a branched structure in the melt results in different molecular weight of the samples, the zero shear viscosity is normalized, according the following assumption:
Janzen and Colby  proposed a method which even works when the molecular weight changes. In their method, they compare the zero shear viscosity of the linear and the branched polymers. The general behavior observed in branched polymers can be described according to:
Where is an average molecular mass between a branch point and its adjacent vertexes, either chain ends or other branch points, A is a parameter that can be evaluated if and of the linear polymer are known and is dependent on according to the following equation :
(2.22) Where B is a constant and for polypropylene is 187.8 g/mole. It is now possible to determine the value of , because and are known constants and and are measured values.
Another indication for branching is given by the relaxation time. The dynamic shear measurements result in curves of the dynamic moduli (G’(ω) and G’’(ω)). At low frequencies, G’ is lower than G’’. The point where G’ crosses over G’’ is the characteristic relaxation time for het polymer, . The addition of branches affects G’ and G’’ and the value of the relaxation time increases with increasing . Therefore, longer indicates higher elasticity and, indirectly, more branching .
A time-temperature superposition can be done to give additional information about the molecular structure of the polymer. The essence of this time-temperature concept is that if all the relaxation phenomena involved in have the same temperature dependency, then changing the temperature of a measurement will have the same effect on the data as shifting the data horizontally on the log(time) or log(frequency) axis . The change in temperature from some reference temperature to a different temperature has the following effect on the relaxation time:
17 where is the horizontally shift factor. The dependence of the time shift factor is most commonly described with the Arrhenius dependence or the WLF dependence, which are given below by equation 2.24 and 2.25
The Arrhenius dependence is used when the temperature is at least hundred degrees above the glass transition temperature, while the WLF dependence provides a better fit of data at temperatures closer to . A horizontal shift alone is often not sufficient to make the relaxation modulus data measured at superpose onto the data measured at . A vertical shift factor is also required and given by the following definition:
where is the density. For linear polymers excellent superposition of both G’ and G’’ can be observed (thermorheological simplicity), while for branched structures superposition for G’ is possible while for G’’ lack of superposition (dispersion) is observed (thermorheological complex) .
Van Gurp-Palmen Analysis
The main idea of the Van Gurp-Palmen analysis is to plot the loss angle versus the magnitude of the complex modulus, . A linear polymer has a loss angle close to 90° which indicates viscous behavior of the polymer. The lower the value of δ, the more solid like (elastic) the material is. Obviously, there is no more information in the van Gurp-Palmen plot then in the usual plot of and versus , but this form of presentation shows the LCB features more transparently and therefore gives a good indication for the formation of branches. Another method that gives a good indication of the elasticity of the samples is plotting the loss angle versus the frequency.
2.3.3 Extensional rheology
An extensional or elongational flow can be defined as deformation that involves stretching along the streamlines . By stretching the polymer material in one direction it undergoes uniaxial extensional flow (figure 5).
Figure 5: Definition diagram for uniaxial extensional flow 
As can be seen in figure 5, a tension (extensional stress) σe and an extension rate can be defined.
Furthermore, with the ratio of the tension and extension rate, the extensional viscosity can be defined:
The stress growth during uniaxial elongation of polymeric melts can be described by several viscoelastic models. One of the most successful models is the Rubber-Like Liquid model of Lodge. By assuming separability of time, this model can be modified to account for nonlinear, strain thinning effects by the incorporation of a damping function to the viscoelastic memory :
In this equation, F is the Finger deformation tensor, h(λ) is the damping function, λ is the stretch as a function of present and past time (λ(t,t’), and µ is the memory function. The memory function, µ, is a material function of time and depends on the relaxation of the melt. The damping function, h(λ), physically signifies the extent of the stress loss due to the reduction of the entanglement density of segmental orientation following the deformation of a given magnitude, λ .
A simple form for the damping function that accommodates the essential phenomenology, the controlled exponential growth of , and LCB effects of variable intensity, is the following :
In this equation β(≥0) is an adjustable parameter that depends on the branching number. Increasing branching number leads to better network connectivity, improved resistance to strain-induced network destruction and, therefore, to less stress damping and smaller β values .
The stretch in uniaxial elongational flow at constant strain rate is: . The damping function of equation 2.29 then becomes :
With this h(λ) Lodge’s Rubber-Like Liquid model with a damping function gives the following for the viscosity growth in uniaxial elongation :
19 (2.31) The non-Newtonian behavior of polymer melts lead to extensional thickening or strain hardening, meaning an increase in viscosity at higher extension rates. The branching number can be estimated by directly measuring the strain hardening. The curves can be fitted by the Lodge’s Rubber-Like Liquid model that implements the damping function (equation 2.31). The estimated model parameters are then used to infer the value of . Gotsis  showed that the parameter β decreases monotonically with the increase of . Therefore the value of β can be used as a measure of the degree of branching.
An empirical relationship between β and the degree of branching is :
with . In other situations it was found that , this indicates that a is not a universal constant but depends on the MWD breadth and the details of branching.
There are many every day and industrial situations where there is a large element of extensional flow. When the extensional viscosity is low, the material will fail when used in industrial applications as foaming, blow moulding and spinning. There are two methods to increase the extensional viscosity of the polymer melt, through branching and broadening the molecular weight. Hereby the extensional viscosity will increase with increasing extension rate. The effect of branching can be seen in figure 6, broadening the molecular weight results in the similar strain hardening behavior.
Figure 6: Effect of branching on the extensional viscosity of polymer melts 
3 Synthesis and characterization of long chain branched i-polypropylene
Long chain branches (LCB) were added to initially linear isotactic-polypropylene (iPP) in the melt through radical reactions. This was carried out in the presence of a free radical initiator (dicumyl peroxide) and selected co-agents. The modified samples were characterized by differential scanning calorimetry (DSC), gel permeation chromatography (GPC) and rheological measurements. Several properties of a co-agent that have significant influence on the obtained structure were defined. Furthermore, the efficiency of the co-agents was evaluated. Hydroquinone (HQ) resulted in modified iPP with the highest degree of branching while allyl-2-furoate (A2F) was not capable of inducing a branched structure.
As noticed in chapter 1 and 2, addition of long chain branches on the iPP backbone significantly improves the process conditions of iPP. The use of LCB-iPP instead of linear iPP enlarges the choice of process techniques. In this report LCB-iPP is produced in the melt through radical reaction. Advantages of producing LCB-iPP in the melt are low cost, simple operation and high productivity; however, one major disadvantage is the difficulty to control the process. The two major side reactions during the process are crosslinking and β-scission. A generally accepted reaction mechanism was already discussed in chapter 2, section 2.2.
There are many factors that have significant influence on the process and the final obtained structure. One of the key factors on the final obtained structure is the used co-agent. A wide range of different co-agents which are capable of inducing a branched structure can be found in existing literature. However, to our knowledge, no systematic study towards the choice of co-agent has been performed. The main aim of this thesis is to evaluate the effectiveness of the several co-agents to induce a branched structure and define properties of the co-agent that have a significant influence on the final structure.
A more accurate understanding of the chemical mechanism involved can give more control over the process and the final structure. Five co-agents were selected in this research and used in combination with dicumyl peroxide (DCP) as radical initiator. The co-agents differ in solubility (in iPP) and reactivity.
Their chemical structure, solubility parameter1, , and the absolute electronegativity difference (of the reactive bonds)2, , are reported in table 1.
1 Calculated by the group contribution method
2 Calculated by HyperChem
21 The first co-agent used in this research is divinylbenzene. Divinylbenzene is selected since it is quite soluble in iPP and the double bonds can easily react with the free macro-radicals that are formed on the iPP chains. A drawback, however, is that divinylbenzene is a self-polymerisable monomer (more reactive towards itself than towards iPP) and is therefore expected to be susceptible towards crosslinking and/or homo-polymerization. This phenomenon was also observed by other researchers  .
Chemical name Abbreviation Chemical structure (cal/cm3)0.5
Divinylbenzene DVB 8.8 0.059
p-Benzoquinone BQ 12.8 0.256
Hydroquinone HQ 15.1 0.250
MBQ 11.1 0.074
Allyl 2-furoate A2F 10.7 0.176
Polypropylene iPP - 7.4 -
Table 1: Information about the used chemicals
The second co-agent that was selected is p-benzoquinone. p-Benzoquinone is highly reactive, but less soluble in iPP in comparison with DVB. A highly reactive co-agent grafts relatively fast on the iPP chain to form the stabilized structure and limits degradation. But according to Parent et al.   the grafting of a co-agent onto the polypropylene chain makes the chain more reactive with respect to molecular weight growth and therefore has a more prominent tendency towards crosslinking.
To suppress crosslinking, β-scission is required to ensure that there are enough shorter iPP chains to react with the grafted adduct. The introduction of an induction time ensures β-scission and the thereby corresponding shorter iPP chains. Based on these arguments, the third selected co-agent is hydroquinone. Hydroquinone is not very soluble in iPP, but is highly reactive and a well-known inhibitor  capable of “consuming” two radicals (figure 7). Hydroquinone need to be converted into p- benzoquinone before it has the desired carbon-carbon double bonds which are required to react with the free macro-radicals on the iPP chain. As a consequence, this gives rise to an induction time.
Furthermore, the conversion of hydroquinone to p-benzoquinone consumes radicals resulting in a decrease in radicals over time and therefore limiting degradation at the end of the process.
Figure 7: Hydroquinone inhibition mechanism
Another approach is the use of a co-agent with two different kinds of carbon-carbon double bonds.
Methyl-p-benzoquinone was therefore chosen as the fourth co-agent in this research. The “highly”
reactive double bond of methyl-p-benzoquinone can react quickly with the free macro-radicals to form the stabilized structure, while the lower reactive double bond can later react with the secondary radical formed through β-scission. This approach results in fast stabilization and a delayed branching reaction.
Furthermore, methyl-p-benzoquinone has a higher solubility in iPP then p-benzoquinone and hydroquinone but is less reactive.
The last selected co-agent is allyl-2-furoate which also has two different kinds of carbon-carbon double bonds, but higher reactivity and solubility in iPP in comparison with methyl-p-benzoquinone.
However, allyl-2-furoate is a self-polymerisable monomer  which, as discussed before, can be a disadvantage and lead to crosslinking and/or homo-polymerization.
This chapter will describe the modification of iPP in the melt through radical reactions and the characterization of the modified material. The characterization of the modified samples was performed by determination of crystallization temperature, molecular weight and gel content. At the end, rheology measurements were used to verify that the LCB really exist on the backbone of the iPP chains.
The isotactic polypropylene was supplied by Sabic, Geleen, in powder form with number average molecular weight (Mn) of 50,172 g/mol, weight average molecular weight (Mw) of 293,013 g/mol and a polydisperisty (Mw/Mn) of 5.84. The powder was stored at -17°C since it didn’t contain any stabilizer.
Divinylbenzene3 (DVB, Aldrich), hydroquinone (HQ, Aldrich), p-benzoquinone (BQ, Aldrich), methyl-p- benzoquinone (MBQ , Aldrich), allyl 2-furoate (A2F, Aldrich), dicumyl peroxide (DCP, Aldrich) and di-tert- butyl p-cresole (BHT, Aldrich) were purchased as high purity products (98%) and were used as received.
3.3.2 Preparation of the samples
The reagents, 37 mmol/kg iPP peroxide (DCP) and 0.025-1 wt% (with respect to iPP) co-agent (DVB, HQ, BQ, MBQ or A2F) were dissolved in acetone. Acetone was chosen because it could dissolve the
3 Purchased with 85% purity
23 reagents but not the polymer and evaporates easily. Cups with the desired amount of peroxide and co- agents were made. Ten gram of iPP was introduced into a Brabender® batch mixer at a temperature of 170°C (5 half times of DCP decomposition4) and a mixing speed of 60 rpm. After 4 minutes at the said temperature, the co-agent was added with a pipette to the melted polymer. After 2 minutes from the addition of the co-agent, peroxide was added with a pipette. After 8 minutes from the addition of the peroxide 0.2 gram of stabilizer (BHT) was added. After 1 minute from the addition of BHT the Brabender was turned off and the polymer melt was removed from the Brabender. All the samples are prepared following this procedure.
3.3.3 Thermal behavior, molecular weight and gel content determination
Differential scanning calorimetry (DSC) was used to determine the crystallization temperature of the samples. The specimens were heated to 200°C at a rate of 10°C/min and remained at 200°C for 5 minutes to eliminate the thermal histories and then cooled down to -50°C with a rate of 10°C/min to determine the crystallization temperature. Then the samples were reheated ones more from -50°C to 200°C still with a rate of 10°C/min to determine the melting point. The scanning is done under nitrogen atmosphere.
Gel permeation chromatography (GPC) was used to determine the molecular weight averages and distribution of the polymer. The samples were dissolved in trichlorobenzene and filtered to remove, when present, the insoluble fraction. The remaining solution was then passed through a PL Gel 5 mL Mixed-A column of the chromatograph at 140°C.
The samples are all extracted in xylene to determine the gel content (cross-linked portion). A weighted amount of the sample, m1 ≈ 1 g, was put into a soxtex thimble and extracted in ± 35 mL boiling xylene in the soxtexTM 2043 apparatus. After extraction for 6 hours (4 hours boiling and 2 hours rinsing) the soxtex thimbles were removed from the soxtex and dried in an oven at 50°C to a constant weight (m2). This weight corresponds to the insoluble (cross-linked) portion of the sample. The amount of cross- linked iPP was then determined from the relation
3.3.4 Dynamic shear measurements
The dynamic shear measurements were performed by a RMS 800 apparatus from Rheometric Scientific. This is a controlled shear rate rheometer, which uses two parallel plates with a diameter of 25 mm and a variable gab. The samples were cut from pressed plates. The granules were pressed to plates at 170°C, close to the melting temperature to avoid air bubbles, for 10 minutes. After 10 minutes the plates were removed and cooled down.
First a dynamic sweep strain measurement was performed at 170°C to determine the linear viscoelastic region and the thereby corresponding applied strain. To be in the viscoelastic region of the samples, the strain varied from 4-220%. Then a temperature/frequency sweep measurement was carried out in a temperature region of 170-230°C and in a frequency range from 0.1-100 rad/s.
4 Calculations can be found in appendix B
24 3.3.5 Extension viscosity measurements
The extensional viscosity was measured with the RME apparatus from Rheometric Scientific. This is a controlled strain rate rheometer. The measurements are performed with rectangular strips of . These strips were cut from pressed plates. The granules were pressed to plates at 170°C, close to the melting temperature to avoid air bubbles, for 10 minutes. After 10 minutes the plates were removed and cooled down.
The strips were placed in the heat chamber (170°C) of the RME apparatus and placed between two clamps surrounded by toothed belts (figure 8). The clamps rotated in opposite direction at a constant elongation rate of 0.1 s-1. The actual strain rate is less than the nominal strain rate that is entered in the RME control program. This is due to some slip at the end of the belts and because the flow profile is never completely uniform. Therefore the stretching of the samples was recorded, so one can determine the formation during the stretching process. The strain rate can then be calculated and the average of the two strain rate is referred to as the true strain rate.
Figure 8: Schematic drawing of RME apparatus5
3.4 Results and discussion
Each co-agent is used to prepare a set of samples whereby the amount of co-agent is adapted. The set of samples are discussed below and arranged according to the used co-agent. Afterwards, the co- agents are compared with each other. There are no results of the extensional viscosity measurements, since the viscosity of the samples was too low to obtain a homogeneous distribution during the measurements.
The mixing torque is measured during the modification in the melt. A remarkable increase in mixing torque is obtained after the addition of the peroxide, around (figure 33 Appendix C). Further analysis showed that the higher the amount of HQ, the longer it takes before the mixing torque increases and eventually the increase in mixing torque completely disappears. This indicates that there is an induction time before any reaction occurs, and this induction time appears to correlate with the amount of HQ that is used. After a given time the mixing torque starts to decrease again. This general trend of mixing torque is in consistency with the findings of Romani et al. . However, they did not
25 find an induction time. The induction time can be explained with the reaction mechanism of HQ (figure 9). Hydroquinone is a well-known inhibitor which is capable of “consuming” two radicals (figure 7) 
and is first converted into p-benzoquinone before it can react with the free macro-radicals on the iPP chain (figure 9) to eventually form the desired branched structure. The higher amount of HQ can result in a longer conversion time towards p-benzoquinone and therefore a longer induction time, however, more research is necessary to verify this hypothesis. When the amount of HQ becomes too high, it is expected that all the radicals are terminated before branching can take place.
The growth of the torque value is caused by the increment of the viscosity, due to the formation of bonds between chains. The decrease of the mixing torque is due to the dispersion of the branched/cross-linked fractions in the not branched/cross-linked matrix .
Figure 9: Reaction mechanism with co-agent hydroquinone (based on  )
After modification with hydroquinone, an increase in crystallization temperature is obtained. After a given amount (>0.4 wt%) of added hydroquinone the crystallization temperature declines again (figure 10). This corresponds with the mixing torque behavior of HQ, where the amount of HQ appears to have effect on the induction time and increase in mixing torque.
26 This increase in crystallization temperature has also been reported in literature   . During the melt modification, degradation, recombination and grafting reactions take place simultaneously.
These reactions result in changes of the following molecular factors :
- Molecular weight and its distribution
- Chain irregularity due to branching/crosslinking, grafting of the co-agent, and/or binding of peroxide radicals to the polymer chain
These changes can affect the thermal behavior of the polymer. The formation of long chain branches results in more nucleation points, it is therefore possible to obtain an increase in crystallization temperature. However, an increase in crystallization temperature can also occur when polypropylene degrades, because degradation leads to more, smaller, chains. These smaller chains act as nucleating points and are capable in raising the crystallization temperature. To enclose this effect, the starting Tc
(HQ = 0 wt%) is from the thermally treated sample (degraded iPP).
Figure 10: Crystallization temperature vs. weight fraction HQ
More insight about the formed structure can be obtained by the molecular weight and the gel content (table 2). On the basis of the purposes and the reaction mechanism (figure 9), it is sufficient to say that an increase in the molecular weight average, in comparison to the reference sample #5, together with an increase in crystallization temperature and no (or low) gel content, indicates the formation of long chain branches. However, since the calibration of the GPC apparatus is performed with polystyrene, the average molecular weight cannot be used as an absolute value but only to show trends.
The mixing torque, crystallization temperature, the trend of Mw average and the zero gel content, indicates that the samples #18, #19, #20, #21 and #53 have a branched structure. To verify the existence of branches shear rheology measurements were performed (figures 11 and 12).
27 Sample # Co-agent Amount of co-
Gel content (%) Mw Mw/Mn
5 - - - 81069 6.2
18 HQ 0.1 0 134648 5.7
19 HQ 0.15 0 145689 6.6
20 HQ 0.2 0 190658 6.5
21 HQ 0.3 0 127540 5.7
53 HQ 0.4 0 n.a. n.a.
45 HQ 0.5 0 137197 6.5
43 HQ 0.8 0 125976 5.6
Table 2: List of samples modified with HQ
The storage modulus, , of all the modified samples is significantly higher at low frequency when compared to the thermally treated sample #5 (figure 11), taken here as reference material. The modified samples show a decrease in the slope of suggesting non-terminal behavior which implies a longer relaxation mechanism, hinting to the possible creation of some long chain branches formed in the melt.
Another way to investigate the presence of LCB involves the examination of the loss angle 
which is plotted versus the frequency. The figure shows an increase in elasticity (decrease in loss angle) when HQ is added, until a certain point (#53 0.4 wt%) when the elasticity declines again (figure 12). This behavior was already expected, due to the consumption of radicals by HQ (figure 7), the results found for the crystallization temperature and the behavior of the mixing torque.
According to literature, linear iPP should display a monotonically decreasing curve of , while for branched samples the curve changes in position and in form .
An increase in elasticity can be obtained due to long chain branches as well as a higher average molecular weight or the broadening of the molecular weight distribution. However, the molecular weight distribution is in the same range for all the samples (table 2). The results (figure 12) are shifted at 170°C (time-temperature superposition) and the samples #18, #20, #21 and #53 show dispersion while the modified samples #45 and #43 show excellent superposition. Dispersion is typical behavior for a branched (or cross-linked) structure, while superposition is typical behavior for linear polymers .
Figure 11: Storage modulus vs. frequency for the linear iPP and the samples modified with HQ (shifted at 170C°)
Figure 12: Loss angle vs. frequency (shifted at 170°C) for iPP melts modified with HQ
All the modified samples show an increase in zero shear viscosity (figure13). The increase in can indicate the formation of branches, but can also be obtained due to a higher molecular weight. The samples #18, #20, #21 and #53 display shear thinning behavior at lower shear rates then the samples #5, #45 and #43. The addition of branches or the broadening of the molecular weight distribution results in a more compact polymer chain and therefore the polymer behaves as a non- Newtonian fluid at lower shear rates . Based on this theory, it is expected that the higher zero shear rate of sample #45 and #43, is created by a higher average molecular weight instead of the introduction of branches.
On the other hand, the rheological behavior in combination with the absence of any gel amount, the mixing torque behavior and the Tc, leads to the conclusion that the samples #18, #20, #21 and #53 have a slightly branched structure. The decrease of branching seems to increase with the amount of HQ present. The only sample that deviates from this trend is #53 with 0.4 wt% HQ. It seems that there is an optimum in the amount of co-agent and any amount above this has an adverse effect on the probability of branches. Borsig et al.  also suggested that there could be an optimum for the amount of co-agent and the probability of branches.
Figure 13: Viscosity vs. frequency for iPP melts modified with HQ
The plastogram (figure 34 Appendix C) shows an increase in mixing torque after the addition of the peroxide and after a certain point the mixing torque decreases again. As discussed before, the increase is caused by the formation of a branched/cross-linked structure and the decrease due to the dispersion of the branched/cross-linked fraction in the not branched/cross-linked matrix.
The DSC measurements show an increase in crystallization temperature after modification with BQ (figure 14). The increase in crystallization temperature can be an indication for some branching. In combination with the measured gel content of these samples (table 3), the conclusion can be drawn that the increase in crystallization temperature of the samples #55, #52 and #41 is obtained due to a cross-linked structure.
Figure 14: Crystallization temperature vs. weight fraction BQ
30 Sample # Co-agent Amount of co-
Gel content (%) Mw Mw/Mn
5 - - 0 81069 6.2
32 BQ 0.1 0 110235 6.0
34 BQ 0.2 0 122997 6.1
35 BQ 0.3 0 125482 5.3
36 BQ 0.4 0 108935 6.4
55 BQ 0.5 58.2 n.a. n.a.
52 BQ 0.6 7.4 n.a. n.a.
41 BQ 0.8 16.8 n.a. n.a.
Table 3: List of samples modified with BQ
A better indication for the formation of LCB is given by the rheology measurements. The storage modulus, , is significantly higher for the samples modified with BQ then for the thermally treated linear sample #5 (figure 15). The absolute value of the elastic moduli seems to increase with the amount of BQ present, but at a given intake (0.4 wt%) the moduli starts to decrease again. This indicates that there is an optimum in the amount of co-agent and any amount above this has an adverse effect on the probability of branches. This trend was also observed when HQ was used as co-agent. The storage modulus of sample #55 is much higher than the storage modulus of the other samples, the high elastic response of this sample is created by the highly cross-linked structure (table 3).
The plot of the loss angle versus the frequency can give a good indication for the presence of branches. The plot is shifted at 170°C (time-temperature superposition) and the samples #34, #35, #36 and #55 show dispersion (figure 16). As discussed before, linear polymers exhibit excellent superposition while a branched structure results in dispersion.
Figure 15: Storage modulus vs. frequency for the linear iPP and the samples modified with BQ (shifted at 170C°)
Figure 16: Loss angle vs. frequency (shifted at 170°C) for iPP melts modified with BQ
These findings are in consistency with the viscosity measurements, where an increase in can be observed for the samples modified with BQ (figure 17). The rheological behavior in combination with the absence of any gel amount, the mixing torque behavior and the increase in Tc, leads to the conclusion
31 that the samples #34, #35 and #36 have a slightly branched structure. Furthermore, the elastic properties of sample #55 are derived from the highly cross-linked structure.
Figure 17: Viscosity vs. frequency for iPP melts modified with BQ
Methyl-p-benzoquinone is a co-agent with two double bonds that differ in reactivity. One “highly”
reactive double bond to quickly stabilize the macro-radicals, and one lower reactive double bond which eventually reacts to form the desired branched structure. The reaction is shown by the increase in mixing torque after the addition of the peroxide (figure 35 Appendix C). The increase is mixing torque is obtained when ≥ 0.2 wt% MBQ is added. From that moment on, there seems to be an induction time which increases when the amount of MBQ increases. An explanation for this might be found in the reaction mechanism (figure 18). First the highly reactive double bond stabilizes the macro-radicals, this reaction does not cause an increase in mixing torque. After a certain point, when (most of) the co-agent is grafted on the macro-radicals, the less reactive double bond starts to react with secondary radicals to form LCB-iPP which causes the increase in mixing torque. To verify this hypothesis, more research needs to be performed.
Figure 18: Reaction mechanism with co-agent methyl-p-benzoquinone
An increase in crystallization temperature is obtained when ≥0.2 wt% MBQ is added (figure 19). This corresponds with the start of the increase in mixing torque. Furthermore, an increase in average molecular weight is obtained without formation of any amount of gel (table 4), thus strongly suggesting the formation of LCB when ≥0.2 wt% MBQ is used.
Figure 19: Crystallization temperature vs. weight fraction MBQ
Sample # Co-agent Amount of co- agent (wt%)
Gel content (%) Mw Mw/Mn
5 - - 0 81069 6.2
51 MBQ 0.075 0 105521 5.8
44 MBQ 0.1 0 92317 5.4
46 MBQ 0.15 0 94461 6.6
47 MBQ 0.2 0 112720 6.3
58 MBQ 0.3 0 129886 6.3
56 MBQ 0.4 0 111101 6.4
57 MBQ 0.8 0 111391 6.0
Table 4: List of samples modified with MBQ
These preliminary conclusions need to be confirmed with rheology measurements, which gives more information on the molecular structure of the modified samples. The curve of the modified samples closely resembles the one for the references iPP (figure 20). Only a minor increase of the storage modulus is obtained when MBQ is used as co-agent. At high amounts of MBQ (0.8 wt%) the slope of decreases and the absolute value increases. When the loss angle is plotted against the frequency and shifted at 170°C, the samples #47, #44, #58 and #56 show some dispersion (figure 21), hinting to the possible creation of some long branches. However, the high value of the loss angle indicates that the destructive effect of the peroxide prevails. Only at high amounts of MBQ the elasticity really increases (sample #57).
Figure 20: Storage modulus vs. frequency for the linear iPP and the samples modified with MBQ (shifted at 170C°)
Figure 21: Loss angle vs. frequency (shifted at 170°C) for iPP melts modified with MBQ
All the samples modified with MBQ show higher values for the dynamic viscosity then the reference sample #5 (figure 22), but they only show a slight increase. The dynamic viscosity increases with the amount of co-agent used. The only sample that deviates from this trend is sample #47. It is not clear why sample #47 deviates from this trend. It can be possible that the reaction has not been carried out successfully, but to verify this, more research needs to be performed.
The mixing torque behavior, increase in crystallization temperature and the increase in molecular weight hint to the formation of long chain branches. As a result, it is expected that the minor increase in elasticity (figure 21) is caused by the formation of some long branches. However, the degradation reaction seems to prevail. At higher levels of MBQ, the formation of long chain branches starts to prevail and an increase in elasticity is obtained (sample #57).
Figure 22: Viscosity vs. frequency for iPP melts modified with MBQ
35 Divinylbenzene (DVB)
The mixing torque increases after the addition of the peroxide (figure 36 Appendix C). The increase in mixing torque becomes bigger with the quantity of DVB used. But then it decreases rather quickly in comparison with the mixing torque behavior when HQ, BQ or MBQ is used as a co-agent. This indicates that the consumption of the co-agent happens fast and that afterwards the only proceeding reaction is degradation. This behavior was also observed by Zhang et al.  when DVB was used as co-agent and by Romani et al.  when a bis maleimide co-agent was used.
An increase in crystallization temperature is obtained when 0.2 wt% DVB or more is added (figure 23). A large increase in average molecular weight is obtained when DVB is used as co-agent and according to the gel content; a cross-linked structure is only obtained when high amounts of DVB are used (table 5).
Figure 23: Crystallization temperature vs. weight fraction DVB
Sample # Co-agent Amount of co- agent (wt%)
Gel content (%) Mw Mw/Mn
5 - - 0 81069 6.2
6 DVB 0.1 0 211241 7.1
7 DVB 0.2 0 197754 7.0
8 DVB 0.3 0 190234 8.5
59 DVB 0.4 0 146977 6.2
60 DVB 0.5 0 199582 6.8
61 DVB 0.8 25.9 197766 7.3
Table 5: List of samples modified with DVB
For the samples #7 and #8 the shape of the curves remains the same as those of the thermally treated linear iPP (sample #5) and no significant increase of the moduli is obtained (figure 24).
They exhibit the typical terminal flow behavior, indicating that they are linear. Sample #6 even shows an
36 increase in the slope of (terminal flow behavior). However, sample #59, #60 and #61 show a decrease in the slope of hinting to the possible formation of branches.
The elasticity of the samples seems to increase with increasing amount of DVB (figure 25). This can be due to introduction of long chain branches, as well as due to a higher average molecular weight or due to broadening of the molecular weight distribution.
Figure 24: Storage modulus vs. frequency for the linear
iPP and the samples modified with DVB (shifted at 170C°) Figure 25: Loss angle vs. frequency (shifted at 170°C) for iPP melts modified with DVB
The samples #7 and #8 show no increase in viscosity (figure 26) which is not in consistency with the GPC data (table 5). An increase in molecular weight should give an increase in according to the following relation:
which was described in chapter 2, section 2.3.2. According to this relation, the increase in viscosity should be higher for all the modified samples when compared to the reference sample #5. Therefore, the GPC data need to be interpreted with caution.
The samples #59, #60 and #61 behave non-Newtonian at lower shear rates. The addition of branches or the broadening of the molecular weight distribution results in a more compact chain and therefore non-Newtonian behavior at lower shear rates . In combination with the gel content found for sample #61, the behavior of sample #61 is caused by a cross-linked structure. While the lower slope of the curve and the decrease in loss angle of the samples #59 and #60, together with the zero gel content and increase in crystallization temperature indicates a slightly branched structure.
Figure 26: Viscosity vs. frequency for iPP melts modified with DVB
The results show that at low levels of DVB, the degradation reaction prevails resulting in a high loss angle (viscous material). While at higher levels of DVB, the crosslinking reaction prevails, this can be seen by the decrease in loss angle and the lower slope of the curve. This behavior was also observed by Borsig et al.  and is expected to be caused by the self-polymerisable ability of DVB.
Allyl-2-furoate has two different kinds of carbon-carbon double bonds and is a self-polymerisable monomer. This can result in the preferred branching reaction or it becomes highly susceptible towards crosslinking and/or homo-polymerization (figure 27).